Suarez was handed his ban on Wednesday after biting Chelsea defender Branislav Ivanovic during a Premier League clash on Sunday, but the Uruguayan has until Friday to appeal.
However, Bean believes it would be counter-productive for Liverpool to chase a reduced suspension, highlighting that the suspension could be increased just as easily.
Bean told talkSPORT: "The problem they have is the only basis they can appeal on is if it's an excessive penalty. That is chaired by an independent chairman and the reality of the situation is that they are walking a tightrope because an appeal panel can actually increase the penalty.
"If I was advising them, I would say to them, ‘take it on the chin, put it behind you and move on’. I think it would be a very risky strategy to appeal against it."
Before being given his ban, Suarez claimed that a standard three-match ban would be sufficient and Bean thinks those comments would have worked against him.
He continued: "I think that was probably the wrong attitude to take. He may well have saved himself a couple of games had he just accepted what he was going to be given and moved on.
"The fact he challenged the FA in saying it wasn’t worth more than three games, when it clearly was, was a mistake. There was no realistic prospect that he was ever going to be successful in that argument."